Gao Mingzhe
Abstract
It is shown that a significant refinement of Hardy-Hilbert's integral inequality can be built by introducing exponential integral with parameter t and by using Bernoulli's inequality as well as improved Hlder's inequality.In particular,for case p=2,a sharp result of the classical Hilbert inequality is obtained.
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It is shown that a significant refinement of Hardy-Hilbert's integral inequality can be built by introducing exponential integral with parameter t and by using Bernoulli's inequality as well as improved Hlder's inequality.In particular,for case p=2,a sharp result of the classical Hilbert inequality is obtained.
Key concepts: Mathematics, Inequality, Bernoulli's inequality, Hölder's inequality, Rearrangement inequality, Kantorovich inequality, Log sum inequality, Exponential function